In this paper, we give an extension of the orthogonality results to dominant operators and p-hyponormal or log-hyponormal operators, also we will generalize some commutativity results. AMS 2000 Mathematics Subject Classification. 47B47, 47A30, 47B20.

Let ?(x) : ?x/2, ?2/3, ?3/4, ?4/5, ... be a sequence with real variable x > 0 and let W?(x) the associated weighted shift weight ?(x). In [17], Exner-Jung-Park provided an algorithm to distinguish weak k-hyponormality of W?(x), obtained sn for some low numbers n = 4,..., 10, such that W?(sn) is weakly n-hyponormal but not n-hyponormal. this paper, we obtain formula (for all positive integer ...

In this paper, we introduce a new class of operators, called k−quasi class An operators, which is a superclass of hyponormal operators and a subclass of (n, k)−quasi−∗−paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that, if T ∈ An then σjp(T ) = σp(T ), σja(T ) = σa(T ) and T − λ has finite ascent for all λ ∈ C. Al...

All extremal solutions of the truncated L-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality. An exponential kernel, arising as the determinantal function of a naturally associated hyponormal operator with rank-one self-commutator, provides a natural de...

Here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. Also we find integers $n$ for which, these groups are $n$-central.

Thompson’s partition of a cyclic subnormal operator into normal and completely non-normal components is combined with non-commutative calculus for hyponormal operators separating outliers from the cloud, in rather general point distributions plane. The main result provides exact transformation formulas power moments prescribed distribution uniform mass carried by cloud. proposed algorithm solel...

The positive definiteness of the exponential transform of a planar domain is proved by elementary means. This direct approach avoids the heavy machinery of the theory of hyponormal operators and leads to a better understanding of the linear data associated in previous works to a quadrature domain. Version: September 10, 2003. 1. The exponential transform Let Ω be a bounded open subset of the co...

For a hyponormal operator, C. R. Putnam’s inequality gives an upper bound on the norm of its self-commutator. In the special case of a Toeplitz operator with analytic symbol in the Smirnov space of a domain, there is also a geometric lower bound shown by D. Khavinson (1985) that when combined with Putnam’s inequality implies the classical isoperimetric inequality. For a nontrivial domain, we co...